How to subtract rational expressions with different denominators - GRE Quantitative Reasoning

Card 1 of 64

Didn't Know

Knew It

1 of 2019 left

Question

Choose the answer which best simplifies the following expression:

$\frac{2x + a}{4}$ - $\frac{3}{2a}$

Tap to reveal answer

Answer

To solve this problem, first multiply each term of the original expression by the denomenator of the other over itself:

$$\frac{2x + a}{4}$($\frac{2a}{2a}$) - $\frac{3}{2a}$($\frac{4}{4}$)$

Then you will have two terms with a common denomenator:

$\frac{4ax + $2a^2$}{8a}$ - $\frac{12}{8a}$

Combine the terms and simplify for your final answer:

$\frac{4ax $+2a^2$ - 12}{8a}$

$\frac{2ax + $a^2$ - 6}{4a}$

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the following expression:

$\frac{2n + 4}{n}$ - $$\frac{n^2$}{5}$

Tap to reveal answer

Answer

To simplify this problem, multiply each term by the denominator of the other over itself:

$$\frac{2n + 4}{n}$\left($\frac{5}{5}\right) - $$\frac{n^2$}{5}$\left($\frac{n}{n}$\right)$

$\frac{10n + 20}{5n}$ - $$\frac{n^3$}{5n}$

Now that both terms share a denominator, you can subtract:

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the following expression:

Tap to reveal answer

Answer

To simplify this expression, first multiply both terms by the denominator of the other over itself:

Now that you have a common denominator, you may subtract:

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the expression below:

Tap to reveal answer

Answer

To simplify this problem, multiply each term by the denomenator of the other over itself:

Then you will yield terms with a like denomenator, which can be combined:

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the expression below:

Tap to reveal answer

Answer

To simplify the expression, first multiply each term by the denomenator of the other over itself:

Then you yield terms with common denomenators, which can be combined:

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the following expression:

Tap to reveal answer

Answer

To simplify, first multiply each of the terms by the denomenator of the other over itself:

Then you will get terms with a common denomenator, which can be combined:

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the expression below:

Tap to reveal answer

Answer

To simplify, first multiply each of the terms by the denomenator of the other over itself:

You will yield terms with a common denomenator, which can be combined:

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the expression below:

$\frac{2a}{14-y}$ - $\frac{3}{8 +a}$

Tap to reveal answer

Answer

To simplify, multiply each of the terms by the denomenator of the other, over itself:

$$\frac{2a}{14-y}$($\frac{8 +a}{8+a}$) - $\frac{3}{8 +a}$($\frac{14-y}{14-y}$)$

You will yield terms with a common denomenator, which can be combined:

$\frac{16a $+2a^2$}{112-8y+14a-ay}$-$\frac{42-3y}{112-8y+14a-ay}$

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the following expression:

$\frac{2n + 4}{n}$ - $$\frac{n^2$}{5}$

Tap to reveal answer

Answer

To simplify this problem, multiply each term by the denominator of the other over itself:

$$\frac{2n + 4}{n}$\left($\frac{5}{5}\right) - $$\frac{n^2$}{5}$\left($\frac{n}{n}$\right)$

$\frac{10n + 20}{5n}$ - $$\frac{n^3$}{5n}$

Now that both terms share a denominator, you can subtract:

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the following expression:

Tap to reveal answer

Answer

To simplify this expression, first multiply both terms by the denominator of the other over itself:

Now that you have a common denominator, you may subtract:

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the following expression:

$\frac{2x + a}{4}$ - $\frac{3}{2a}$

Tap to reveal answer

Answer

To solve this problem, first multiply each term of the original expression by the denomenator of the other over itself:

$$\frac{2x + a}{4}$($\frac{2a}{2a}$) - $\frac{3}{2a}$($\frac{4}{4}$)$

Then you will have two terms with a common denomenator:

$\frac{4ax + $2a^2$}{8a}$ - $\frac{12}{8a}$

Combine the terms and simplify for your final answer:

$\frac{4ax $+2a^2$ - 12}{8a}$

$\frac{2ax + $a^2$ - 6}{4a}$

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the expression below:

Tap to reveal answer

Answer

To simplify this problem, multiply each term by the denomenator of the other over itself:

Then you will yield terms with a like denomenator, which can be combined:

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the expression below:

Tap to reveal answer

Answer

To simplify the expression, first multiply each term by the denomenator of the other over itself:

Then you yield terms with common denomenators, which can be combined:

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the following expression:

Tap to reveal answer

Answer

To simplify, first multiply each of the terms by the denomenator of the other over itself:

Then you will get terms with a common denomenator, which can be combined:

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the expression below:

Tap to reveal answer

Answer

To simplify, first multiply each of the terms by the denomenator of the other over itself:

You will yield terms with a common denomenator, which can be combined:

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the expression below:

$\frac{2a}{14-y}$ - $\frac{3}{8 +a}$

Tap to reveal answer

Answer

To simplify, multiply each of the terms by the denomenator of the other, over itself:

$$\frac{2a}{14-y}$($\frac{8 +a}{8+a}$) - $\frac{3}{8 +a}$($\frac{14-y}{14-y}$)$

You will yield terms with a common denomenator, which can be combined:

$\frac{16a $+2a^2$}{112-8y+14a-ay}$-$\frac{42-3y}{112-8y+14a-ay}$

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the following expression:

$\frac{2x + a}{4}$ - $\frac{3}{2a}$

Tap to reveal answer

Answer

To solve this problem, first multiply each term of the original expression by the denomenator of the other over itself:

$$\frac{2x + a}{4}$($\frac{2a}{2a}$) - $\frac{3}{2a}$($\frac{4}{4}$)$

Then you will have two terms with a common denomenator:

$\frac{4ax + $2a^2$}{8a}$ - $\frac{12}{8a}$

Combine the terms and simplify for your final answer:

$\frac{4ax $+2a^2$ - 12}{8a}$

$\frac{2ax + $a^2$ - 6}{4a}$

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the following expression:

$\frac{2n + 4}{n}$ - $$\frac{n^2$}{5}$

Tap to reveal answer

Answer

To simplify this problem, multiply each term by the denominator of the other over itself:

$$\frac{2n + 4}{n}$\left($\frac{5}{5}\right) - $$\frac{n^2$}{5}$\left($\frac{n}{n}$\right)$

$\frac{10n + 20}{5n}$ - $$\frac{n^3$}{5n}$

Now that both terms share a denominator, you can subtract:

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the following expression:

Tap to reveal answer

Answer

To simplify this expression, first multiply both terms by the denominator of the other over itself:

Now that you have a common denominator, you may subtract:

← Didn't Know|Knew It →

Question

Choose the answer which best simplifies the expression below:

Tap to reveal answer

Answer

To simplify this problem, multiply each term by the denomenator of the other over itself:

Then you will yield terms with a like denomenator, which can be combined:

← Didn't Know|Knew It →

Knew It

How to subtract rational expressions with different denominators - GRE Quantitative Reasoning

Choose the answer which best simplifies the following expression:

To solve this problem, first multiply each term of the original expression by the denomenator of the other over itself: Then you will have two terms with a common denomenator: Combine the terms and simplify for your final answer:

Choose the answer which best simplifies the following expression:

To simplify this problem, multiply each term by the denominator of the other over itself: Now that both terms share a denominator, you can subtract:

Choose the answer which best simplifies the following expression:

To simplify this expression, first multiply both terms by the denominator of the other over itself: Now that you have a common denominator, you may subtract:

Choose the answer which best simplifies the expression below:

To simplify this problem, multiply each term by the denomenator of the other over itself: Then you will yield terms with a like denomenator, which can be combined:

Choose the answer which best simplifies the expression below:

To simplify the expression, first multiply each term by the denomenator of the other over itself: Then you yield terms with common denomenators, which can be combined:

Choose the answer which best simplifies the following expression:

To simplify, first multiply each of the terms by the denomenator of the other over itself: Then you will get terms with a common denomenator, which can be combined:

Choose the answer which best simplifies the expression below:

To simplify, first multiply each of the terms by the denomenator of the other over itself: You will yield terms with a common denomenator, which can be combined:

Choose the answer which best simplifies the expression below:

To simplify, multiply each of the terms by the denomenator of the other, over itself: You will yield terms with a common denomenator, which can be combined:

Choose the answer which best simplifies the following expression:

To simplify this problem, multiply each term by the denominator of the other over itself: Now that both terms share a denominator, you can subtract:

Choose the answer which best simplifies the following expression:

To simplify this expression, first multiply both terms by the denominator of the other over itself: Now that you have a common denominator, you may subtract:

Choose the answer which best simplifies the following expression:

To solve this problem, first multiply each term of the original expression by the denomenator of the other over itself: Then you will have two terms with a common denomenator: Combine the terms and simplify for your final answer:

Choose the answer which best simplifies the expression below:

To simplify this problem, multiply each term by the denomenator of the other over itself: Then you will yield terms with a like denomenator, which can be combined:

Choose the answer which best simplifies the expression below:

To simplify the expression, first multiply each term by the denomenator of the other over itself: Then you yield terms with common denomenators, which can be combined:

Choose the answer which best simplifies the following expression:

To simplify, first multiply each of the terms by the denomenator of the other over itself: Then you will get terms with a common denomenator, which can be combined:

Choose the answer which best simplifies the expression below:

To simplify, first multiply each of the terms by the denomenator of the other over itself: You will yield terms with a common denomenator, which can be combined:

Choose the answer which best simplifies the expression below:

To simplify, multiply each of the terms by the denomenator of the other, over itself: You will yield terms with a common denomenator, which can be combined:

Choose the answer which best simplifies the following expression:

To solve this problem, first multiply each term of the original expression by the denomenator of the other over itself: Then you will have two terms with a common denomenator: Combine the terms and simplify for your final answer:

Choose the answer which best simplifies the following expression:

To simplify this problem, multiply each term by the denominator of the other over itself: Now that both terms share a denominator, you can subtract:

Choose the answer which best simplifies the following expression:

To simplify this expression, first multiply both terms by the denominator of the other over itself: Now that you have a common denominator, you may subtract:

Choose the answer which best simplifies the expression below:

To simplify this problem, multiply each term by the denomenator of the other over itself: Then you will yield terms with a like denomenator, which can be combined:

Choose the answer which best simplifies the following expression:

$\frac{2x + a}{4}$ - $\frac{3}{2a}$

Choose the answer which best simplifies the following expression:

$\frac{2n + 4}{n}$ - $$\frac{n^2$}{5}$

To simplify this problem, multiply each term by the denominator of the other over itself:

$$\frac{2n + 4}{n}$\left($\frac{5}{5}\right) - $$\frac{n^2$}{5}$\left($\frac{n}{n}$\right)$

$\frac{10n + 20}{5n}$ - $$\frac{n^3$}{5n}$

Now that both terms share a denominator, you can subtract:

To simplify this expression, first multiply both terms by the denominator of the other over itself:

Now that you have a common denominator, you may subtract:

To simplify this problem, multiply each term by the denomenator of the other over itself:

Then you will yield terms with a like denomenator, which can be combined:

To simplify the expression, first multiply each term by the denomenator of the other over itself:

Then you yield terms with common denomenators, which can be combined:

To simplify, first multiply each of the terms by the denomenator of the other over itself:

Then you will get terms with a common denomenator, which can be combined:

To simplify, first multiply each of the terms by the denomenator of the other over itself:

You will yield terms with a common denomenator, which can be combined:

Choose the answer which best simplifies the expression below:

$\frac{2a}{14-y}$ - $\frac{3}{8 +a}$

Choose the answer which best simplifies the following expression:

$\frac{2n + 4}{n}$ - $$\frac{n^2$}{5}$

To simplify this problem, multiply each term by the denominator of the other over itself:

$$\frac{2n + 4}{n}$\left($\frac{5}{5}\right) - $$\frac{n^2$}{5}$\left($\frac{n}{n}$\right)$

$\frac{10n + 20}{5n}$ - $$\frac{n^3$}{5n}$

Now that both terms share a denominator, you can subtract:

To simplify this expression, first multiply both terms by the denominator of the other over itself:

Now that you have a common denominator, you may subtract:

Choose the answer which best simplifies the following expression:

$\frac{2x + a}{4}$ - $\frac{3}{2a}$

To simplify this problem, multiply each term by the denomenator of the other over itself:

Then you will yield terms with a like denomenator, which can be combined:

To simplify the expression, first multiply each term by the denomenator of the other over itself:

Then you yield terms with common denomenators, which can be combined:

To simplify, first multiply each of the terms by the denomenator of the other over itself:

Then you will get terms with a common denomenator, which can be combined:

To simplify, first multiply each of the terms by the denomenator of the other over itself:

You will yield terms with a common denomenator, which can be combined:

Choose the answer which best simplifies the expression below:

$\frac{2a}{14-y}$ - $\frac{3}{8 +a}$

Choose the answer which best simplifies the following expression:

$\frac{2x + a}{4}$ - $\frac{3}{2a}$

Choose the answer which best simplifies the following expression:

$\frac{2n + 4}{n}$ - $$\frac{n^2$}{5}$

To simplify this problem, multiply each term by the denominator of the other over itself:

$$\frac{2n + 4}{n}$\left($\frac{5}{5}\right) - $$\frac{n^2$}{5}$\left($\frac{n}{n}$\right)$

$\frac{10n + 20}{5n}$ - $$\frac{n^3$}{5n}$

Now that both terms share a denominator, you can subtract:

To simplify this expression, first multiply both terms by the denominator of the other over itself:

Now that you have a common denominator, you may subtract:

To simplify this problem, multiply each term by the denomenator of the other over itself:

Then you will yield terms with a like denomenator, which can be combined: